thermoviscoelastic

Thermoviscoelasticity is a branch of continuum mechanics that studies materials whose mechanical response depends on temperature and exhibits time-dependent (viscoelastic) behavior, with coupling between thermal and mechanical fields. In these materials, stress depends on the history of strain and temperature, and conversely, temperature can be affected by mechanical loading through dissipative heating.

The constitutive description combines viscoelastic and thermal effects. In linear thermoviscoelasticity, the stress at time t is given by a convolution of a temperature-dependent relaxation function G(t−τ, T) with the strain rate, plus potential thermal stresses due to temperature changes. The total strain is the sum of an elastic, a viscoelastic (time-dependent) part, and a thermal strain proportional to the temperature change via a coefficient α. The theory satisfies energy balance and the second law, ensuring dissipation.

A common modeling approach uses generalized Maxwell or Voigt elements with temperature-dependent moduli and relaxation times, or internal-variable formalisms. Temperature dependence is often captured via time-temperature superposition, enabling a master curve through shift factors aT (e.g., Williams-Landel-Ferry) but with limitations near phase transitions or large temperature changes.

Applications include polymers, adhesives, coatings, asphalt, rubbers, and biological tissues, where accurate prediction of damping, creep, stress relaxation, and thermal expansion under variable temperature is important. Experimental characterization frequently combines dynamic mechanical analysis across temperatures, creep tests with temperature ramps, and calorimetric data to inform the temperature dependence of material properties. Numerical implementations commonly couple thermo-viscoelastic constitutive models with heat conduction in finite-element analyses.